
package Jama;

import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.text.DecimalFormat;
import java.text.DecimalFormatSymbols;
import java.text.NumberFormat;
import java.util.Locale;

import Jama.util.Maths;

/**
 * Jama = Java Matrix class.
 * <P>
 * The Java Matrix Class provides the fundamental operations of numerical linear
 * algebra. Various constructors create Matrices from two dimensional arrays of
 * double precision floating point numbers. Various "gets" and "sets" provide
 * access to submatrices and matrix elements. Several methods implement basic
 * matrix arithmetic, including matrix addition and multiplication, matrix
 * norms, and element-by-element array operations. Methods for reading and
 * printing matrices are also included. All the operations in this version of
 * the Matrix Class involve real matrices. Complex matrices may be handled in a
 * future version.
 * <P>
 * Five fundamental matrix decompositions, which consist of pairs or triples of
 * matrices, permutation vectors, and the like, produce results in five
 * decomposition classes. These decompositions are accessed by the Matrix class
 * to compute solutions of simultaneous linear equations, determinants, inverses
 * and other matrix functions. The five decompositions are:
 * <P>
 * <UL>
 * <LI>Cholesky Decomposition of symmetric, positive definite matrices.
 * <LI>LU Decomposition of rectangular matrices.
 * <LI>QR Decomposition of rectangular matrices.
 * <LI>Singular Value Decomposition of rectangular matrices.
 * <LI>Eigenvalue Decomposition of both symmetric and nonsymmetric square
 * matrices.
 * </UL>
 * <DL>
 * <DT><B>Example of use:</B></DT>
 * <P>
 * <DD>Solve a linear system A x = b and compute the residual norm, ||b - A
 * x||.
 * <P>
 * 
 * <PRE>
 * double[][] vals = { { 1., 2., 3 }, { 4., 5., 6. }, { 7., 8., 10. } };
 * 
 * Matrix A = new Matrix(vals);
 * 
 * Matrix b = Matrix.random(3, 1);
 * 
 * Matrix x = A.solve(b);
 * 
 * Matrix r = A.times(x).minus(b);
 * 
 * double rnorm = r.normInf();
 * </PRE>
 * 
 * </DD>
 * </DL>
 * 
 * @author The MathWorks, Inc. and the National Institute of Standards and
 *         Technology.
 * @version 5 August 1998
 */

public class Matrix implements Cloneable, java.io.Serializable {

    /*
     * ------------------------ Class variables ------------------------
     */

    /**
     * Construct a matrix from a copy of a 2-D array.
     * 
     * @param A
     *            Two-dimensional array of doubles.
     * @exception IllegalArgumentException
     *                All rows must have the same length
     */

    public static Matrix constructWithCopy(double[][] A) {

        int m = A.length;
        int n = A[0].length;
        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            if (A[i].length != n) {
                throw new IllegalArgumentException(
                        "All rows must have the same length.");
            }
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j];
            }
        }
        return X;
    }

    /**
     * Generate identity matrix
     * 
     * @param m
     *            Number of rows.
     * @param n
     *            Number of colums.
     * @return An m-by-n matrix with ones on the diagonal and zeros elsewhere.
     */

    public static Matrix identity(int m, int n) {

        Matrix A = new Matrix(m, n);
        double[][] X = A.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                X[i][j] = (i == j ? 1.0 : 0.0);
            }
        }
        return A;
    }

    /*
     * ------------------------ Constructors ------------------------
     */

    /**
     * Generate matrix with random elements
     * 
     * @param m
     *            Number of rows.
     * @param n
     *            Number of colums.
     * @return An m-by-n matrix with uniformly distributed random elements.
     */

    public static Matrix random(int m, int n) {

        Matrix A = new Matrix(m, n);
        double[][] X = A.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                X[i][j] = Math.random();
            }
        }
        return A;
    }

    /**
     * Read a matrix from a stream. The format is the same the print method, so
     * printed matrices can be read back in (provided they were printed using US
     * Locale). Elements are separated by whitespace, all the elements for each
     * row appear on a single line, the last row is followed by a blank line.
     * 
     * @param input
     *            the input stream.
     */

    public static Matrix read(BufferedReader input) throws java.io.IOException {

        StreamTokenizer tokenizer = new StreamTokenizer(input);

        // Although StreamTokenizer will parse numbers, it doesn't recognize
        // scientific notation (E or D); however, Double.valueOf does.
        // The strategy here is to disable StreamTokenizer's number parsing.
        // We'll only get whitespace delimited words, EOL's and EOF's.
        // These words should all be numbers, for Double.valueOf to parse.

        tokenizer.resetSyntax();
        tokenizer.wordChars(0, 255);
        tokenizer.whitespaceChars(0, ' ');
        tokenizer.eolIsSignificant(true);
        java.util.Vector v = new java.util.Vector();

        // Ignore initial empty lines
        while (tokenizer.nextToken() == StreamTokenizer.TT_EOL) {
            ;
        }
        if (tokenizer.ttype == StreamTokenizer.TT_EOF) {
            throw new java.io.IOException("Unexpected EOF on matrix read.");
        }
        do {
            v.addElement(Double.valueOf(tokenizer.sval)); // Read & store 1st
            // row.
        } while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);

        int n = v.size(); // Now we've got the number of columns!
        double row[] = new double[n];
        for (int j = 0; j < n; j++) {
            row[j] = ((Double) v.elementAt(j)).doubleValue();
        }
        v.removeAllElements();
        v.addElement(row); // Start storing rows instead of columns.
        while (tokenizer.nextToken() == StreamTokenizer.TT_WORD) {
            // While non-empty lines
            v.addElement(row = new double[n]);
            int j = 0;
            do {
                if (j >= n) {
                    throw new java.io.IOException("Row " + v.size()
                            + " is too long.");
                }
                row[j++] = Double.valueOf(tokenizer.sval).doubleValue();
            } while (tokenizer.nextToken() == StreamTokenizer.TT_WORD);
            if (j < n) {
                throw new java.io.IOException("Row " + v.size()
                        + " is too short.");
            }
        }
        int m = v.size(); // Now we've got the number of rows.
        double[][] A = new double[m][];
        v.copyInto(A); // copy the rows out of the vector
        return new Matrix(A);
    }

    /**
     * Array for internal storage of elements.
     * 
     * @serial internal array storage.
     */
    private double[][] A;

    /**
     * Row and column dimensions.
     * 
     * @serial row dimension.
     * @serial column dimension.
     */
    private int m, n;

    /**
     * Construct a matrix from a one-dimensional packed array
     * 
     * @param vals
     *            One-dimensional array of doubles, packed by columns (ala
     *            Fortran).
     * @param m
     *            Number of rows.
     * @exception IllegalArgumentException
     *                Array length must be a multiple of m.
     */

    public Matrix(double vals[], int m) {

        this.m = m;
        n = (m != 0 ? vals.length / m : 0);
        if (m * n != vals.length) {
            throw new IllegalArgumentException(
                    "Array length must be a multiple of m.");
        }
        A = new double[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = vals[i + j * m];
            }
        }
    }

    /*
     * ------------------------ Public Methods ------------------------
     */

    /**
     * Construct a matrix from a 2-D array.
     * 
     * @param A
     *            Two-dimensional array of doubles.
     * @exception IllegalArgumentException
     *                All rows must have the same length
     * @see #constructWithCopy
     */

    public Matrix(double[][] A) {

        m = A.length;
        n = A[0].length;
        for (int i = 0; i < m; i++) {
            if (A[i].length != n) {
                throw new IllegalArgumentException(
                        "All rows must have the same length.");
            }
        }
        this.A = A;
    }

    /**
     * Construct a matrix quickly without checking arguments.
     * 
     * @param A
     *            Two-dimensional array of doubles.
     * @param m
     *            Number of rows.
     * @param n
     *            Number of colums.
     */

    public Matrix(double[][] A, int m, int n) {

        this.A = A;
        this.m = m;
        this.n = n;
    }

    /**
     * Construct an m-by-n matrix of zeros.
     * 
     * @param m
     *            Number of rows.
     * @param n
     *            Number of colums.
     */

    public Matrix(int m, int n) {

        this.m = m;
        this.n = n;
        A = new double[m][n];
    }

    /**
     * Construct an m-by-n constant matrix.
     * 
     * @param m
     *            Number of rows.
     * @param n
     *            Number of colums.
     * @param s
     *            Fill the matrix with this scalar value.
     */

    public Matrix(int m, int n, double s) {

        this.m = m;
        this.n = n;
        A = new double[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = s;
            }
        }
    }

    /**
     * Element-by-element left division, C = A.\B
     * 
     * @param B
     *            another matrix
     * @return A.\B
     */

    public Matrix arrayLeftDivide(Matrix B) {

        checkMatrixDimensions(B);
        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = B.A[i][j] / A[i][j];
            }
        }
        return X;
    }

    /**
     * Element-by-element left division in place, A = A.\B
     * 
     * @param B
     *            another matrix
     * @return A.\B
     */

    public Matrix arrayLeftDivideEquals(Matrix B) {

        checkMatrixDimensions(B);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = B.A[i][j] / A[i][j];
            }
        }
        return this;
    }

    /**
     * Element-by-element right division, C = A./B
     * 
     * @param B
     *            another matrix
     * @return A./B
     */

    public Matrix arrayRightDivide(Matrix B) {

        checkMatrixDimensions(B);
        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j] / B.A[i][j];
            }
        }
        return X;
    }

    /**
     * Element-by-element right division in place, A = A./B
     * 
     * @param B
     *            another matrix
     * @return A./B
     */

    public Matrix arrayRightDivideEquals(Matrix B) {

        checkMatrixDimensions(B);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = A[i][j] / B.A[i][j];
            }
        }
        return this;
    }

    /**
     * Element-by-element multiplication, C = A.*B
     * 
     * @param B
     *            another matrix
     * @return A.*B
     */

    public Matrix arrayTimes(Matrix B) {

        checkMatrixDimensions(B);
        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j] * B.A[i][j];
            }
        }
        return X;
    }

    /**
     * Element-by-element multiplication in place, A = A.*B
     * 
     * @param B
     *            another matrix
     * @return A.*B
     */

    public Matrix arrayTimesEquals(Matrix B) {

        checkMatrixDimensions(B);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = A[i][j] * B.A[i][j];
            }
        }
        return this;
    }

    /** Check if size(A) == size(B) * */

    private void checkMatrixDimensions(Matrix B) {

        if (B.m != m || B.n != n) {
            throw new IllegalArgumentException("Matrix dimensions must agree.");
        }
    }

    /**
     * Cholesky Decomposition
     * 
     * @return CholeskyDecomposition
     * @see CholeskyDecomposition
     */

    public CholeskyDecomposition chol() {

        return new CholeskyDecomposition(this);
    }

    /**
     * Clone the Matrix object.
     */

    @Override
    public Object clone() {

        return this.copy();
    }

    /**
     * Matrix condition (2 norm)
     * 
     * @return ratio of largest to smallest singular value.
     */

    public double cond() {

        return new SingularValueDecomposition(this).cond();
    }

    /**
     * Make a deep copy of a matrix
     */

    public Matrix copy() {

        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j];
            }
        }
        return X;
    }

    /**
     * Matrix determinant
     * 
     * @return determinant
     */

    public double det() {

        return new LUDecomposition(this).det();
    }

    /**
     * Eigenvalue Decomposition
     * 
     * @return EigenvalueDecomposition
     * @see EigenvalueDecomposition
     */

    public EigenvalueDecomposition eig() {

        return new EigenvalueDecomposition(this);
    }

    /**
     * Get a single element.
     * 
     * @param i
     *            Row index.
     * @param j
     *            Column index.
     * @return A(i,j)
     * @exception ArrayIndexOutOfBoundsException
     */

    public double get(int i, int j) {

        return A[i][j];
    }

    /**
     * Access the internal two-dimensional array.
     * 
     * @return Pointer to the two-dimensional array of matrix elements.
     */

    public double[][] getArray() {

        return A;
    }

    /**
     * Copy the internal two-dimensional array.
     * 
     * @return Two-dimensional array copy of matrix elements.
     */

    public double[][] getArrayCopy() {

        double[][] C = new double[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j];
            }
        }
        return C;
    }

    /**
     * Get column dimension.
     * 
     * @return n, the number of columns.
     */

    public int getColumnDimension() {

        return n;
    }

    /**
     * Make a one-dimensional column packed copy of the internal array.
     * 
     * @return Matrix elements packed in a one-dimensional array by columns.
     */

    public double[] getColumnPackedCopy() {

        double[] vals = new double[m * n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                vals[i + j * m] = A[i][j];
            }
        }
        return vals;
    }

    /**
     * Get a submatrix.
     * 
     * @param i0
     *            Initial row index
     * @param i1
     *            Final row index
     * @param j0
     *            Initial column index
     * @param j1
     *            Final column index
     * @return A(i0:i1,j0:j1)
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public Matrix getMatrix(int i0, int i1, int j0, int j1) {

        Matrix X = new Matrix(i1 - i0 + 1, j1 - j0 + 1);
        double[][] B = X.getArray();
        try {
            for (int i = i0; i <= i1; i++) {
                for (int j = j0; j <= j1; j++) {
                    B[i - i0][j - j0] = A[i][j];
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
        return X;
    }

    /**
     * Get a submatrix.
     * 
     * @param i0
     *            Initial row index
     * @param i1
     *            Final row index
     * @param c
     *            Array of column indices.
     * @return A(i0:i1,c(:))
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public Matrix getMatrix(int i0, int i1, int[] c) {

        Matrix X = new Matrix(i1 - i0 + 1, c.length);
        double[][] B = X.getArray();
        try {
            for (int i = i0; i <= i1; i++) {
                for (int j = 0; j < c.length; j++) {
                    B[i - i0][j] = A[i][c[j]];
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
        return X;
    }

    /**
     * Get a submatrix.
     * 
     * @param r
     *            Array of row indices.
     * @param i0
     *            Initial column index
     * @param i1
     *            Final column index
     * @return A(r(:),j0:j1)
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public Matrix getMatrix(int[] r, int j0, int j1) {

        Matrix X = new Matrix(r.length, j1 - j0 + 1);
        double[][] B = X.getArray();
        try {
            for (int i = 0; i < r.length; i++) {
                for (int j = j0; j <= j1; j++) {
                    B[i][j - j0] = A[r[i]][j];
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
        return X;
    }

    /**
     * Get a submatrix.
     * 
     * @param r
     *            Array of row indices.
     * @param c
     *            Array of column indices.
     * @return A(r(:),c(:))
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public Matrix getMatrix(int[] r, int[] c) {

        Matrix X = new Matrix(r.length, c.length);
        double[][] B = X.getArray();
        try {
            for (int i = 0; i < r.length; i++) {
                for (int j = 0; j < c.length; j++) {
                    B[i][j] = A[r[i]][c[j]];
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
        return X;
    }

    /**
     * Get row dimension.
     * 
     * @return m, the number of rows.
     */

    public int getRowDimension() {

        return m;
    }

    /**
     * Make a one-dimensional row packed copy of the internal array.
     * 
     * @return Matrix elements packed in a one-dimensional array by rows.
     */

    public double[] getRowPackedCopy() {

        double[] vals = new double[m * n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                vals[i * n + j] = A[i][j];
            }
        }
        return vals;
    }

    /**
     * Matrix inverse or pseudoinverse
     * 
     * @return inverse(A) if A is square, pseudoinverse otherwise.
     */

    public Matrix inverse() {

        return solve(identity(m, m));
    }

    /**
     * LU Decomposition
     * 
     * @return LUDecomposition
     * @see LUDecomposition
     */

    public LUDecomposition lu() {

        return new LUDecomposition(this);
    }

    /**
     * C = A - B
     * 
     * @param B
     *            another matrix
     * @return A - B
     */

    public Matrix minus(Matrix B) {

        checkMatrixDimensions(B);
        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j] - B.A[i][j];
            }
        }
        return X;
    }

    /**
     * A = A - B
     * 
     * @param B
     *            another matrix
     * @return A - B
     */

    public Matrix minusEquals(Matrix B) {

        checkMatrixDimensions(B);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = A[i][j] - B.A[i][j];
            }
        }
        return this;
    }

    /**
     * One norm
     * 
     * @return maximum column sum.
     */

    public double norm1() {

        double f = 0;
        for (int j = 0; j < n; j++) {
            double s = 0;
            for (int i = 0; i < m; i++) {
                s += Math.abs(A[i][j]);
            }
            f = Math.max(f, s);
        }
        return f;
    }

    /**
     * Two norm
     * 
     * @return maximum singular value.
     */

    public double norm2() {

        return (new SingularValueDecomposition(this).norm2());
    }

    /**
     * Frobenius norm
     * 
     * @return sqrt of sum of squares of all elements.
     */

    public double normF() {

        double f = 0;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                f = Maths.hypot(f, A[i][j]);
            }
        }
        return f;
    }

    /**
     * Infinity norm
     * 
     * @return maximum row sum.
     */

    public double normInf() {

        double f = 0;
        for (int i = 0; i < m; i++) {
            double s = 0;
            for (int j = 0; j < n; j++) {
                s += Math.abs(A[i][j]);
            }
            f = Math.max(f, s);
        }
        return f;
    }

    /**
     * C = A + B
     * 
     * @param B
     *            another matrix
     * @return A + B
     */

    public Matrix plus(Matrix B) {

        checkMatrixDimensions(B);
        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = A[i][j] + B.A[i][j];
            }
        }
        return X;
    }

    /**
     * A = A + B
     * 
     * @param B
     *            another matrix
     * @return A + B
     */

    public Matrix plusEquals(Matrix B) {

        checkMatrixDimensions(B);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = A[i][j] + B.A[i][j];
            }
        }
        return this;
    }

    /**
     * Print the matrix to stdout. Line the elements up in columns with a
     * Fortran-like 'Fw.d' style format.
     * 
     * @param w
     *            Column width.
     * @param d
     *            Number of digits after the decimal.
     */

    public void print(int w, int d) {

        print(new PrintWriter(System.out, true), w, d);
    }

    /**
     * Print the matrix to stdout. Line the elements up in columns. Use the
     * format object, and right justify within columns of width characters. Note
     * that is the matrix is to be read back in, you probably will want to use a
     * NumberFormat that is set to US Locale.
     * 
     * @param format
     *            A Formatting object for individual elements.
     * @param width
     *            Field width for each column.
     * @see java.text.DecimalFormat#setDecimalFormatSymbols
     */

    public void print(NumberFormat format, int width) {

        print(new PrintWriter(System.out, true), format, width);
    }

    /**
     * Print the matrix to the output stream. Line the elements up in columns
     * with a Fortran-like 'Fw.d' style format.
     * 
     * @param output
     *            Output stream.
     * @param w
     *            Column width.
     * @param d
     *            Number of digits after the decimal.
     */

    public void print(PrintWriter output, int w, int d) {

        DecimalFormat format = new DecimalFormat();
        format.setDecimalFormatSymbols(new DecimalFormatSymbols(Locale.US));
        format.setMinimumIntegerDigits(1);
        format.setMaximumFractionDigits(d);
        format.setMinimumFractionDigits(d);
        format.setGroupingUsed(false);
        print(output, format, w + 2);
    }

    /**
     * Print the matrix to the output stream. Line the elements up in columns.
     * Use the format object, and right justify within columns of width
     * characters. Note that is the matrix is to be read back in, you probably
     * will want to use a NumberFormat that is set to US Locale.
     * 
     * @param output
     *            the output stream.
     * @param format
     *            A formatting object to format the matrix elements
     * @param width
     *            Column width.
     * @see java.text.DecimalFormat#setDecimalFormatSymbols
     */

    public void print(PrintWriter output, NumberFormat format, int width) {

        output.println(); // start on new line.
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                String s = format.format(A[i][j]); // format the number
                int padding = Math.max(1, width - s.length()); // At _least_ 1
                // space
                for (int k = 0; k < padding; k++) {
                    output.print(' ');
                }
                output.print(s);
            }
            output.println();
        }
        output.println(); // end with blank line.
    }

    /**
     * QR Decomposition
     * 
     * @return QRDecomposition
     * @see QRDecomposition
     */

    public QRDecomposition qr() {

        return new QRDecomposition(this);
    }

    /**
     * Matrix rank
     * 
     * @return effective numerical rank, obtained from SVD.
     */

    public int rank() {

        return new SingularValueDecomposition(this).rank();
    }

    /**
     * Set a single element.
     * 
     * @param i
     *            Row index.
     * @param j
     *            Column index.
     * @param s
     *            A(i,j).
     * @exception ArrayIndexOutOfBoundsException
     */

    public void set(int i, int j, double s) {

        A[i][j] = s;
    }

    /**
     * Set a submatrix.
     * 
     * @param i0
     *            Initial row index
     * @param i1
     *            Final row index
     * @param j0
     *            Initial column index
     * @param j1
     *            Final column index
     * @param X
     *            A(i0:i1,j0:j1)
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public void setMatrix(int i0, int i1, int j0, int j1, Matrix X) {

        try {
            for (int i = i0; i <= i1; i++) {
                for (int j = j0; j <= j1; j++) {
                    A[i][j] = X.get(i - i0, j - j0);
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
    }

    /**
     * Set a submatrix.
     * 
     * @param i0
     *            Initial row index
     * @param i1
     *            Final row index
     * @param c
     *            Array of column indices.
     * @param X
     *            A(i0:i1,c(:))
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public void setMatrix(int i0, int i1, int[] c, Matrix X) {

        try {
            for (int i = i0; i <= i1; i++) {
                for (int j = 0; j < c.length; j++) {
                    A[i][c[j]] = X.get(i - i0, j);
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
    }

    /**
     * Set a submatrix.
     * 
     * @param r
     *            Array of row indices.
     * @param j0
     *            Initial column index
     * @param j1
     *            Final column index
     * @param X
     *            A(r(:),j0:j1)
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public void setMatrix(int[] r, int j0, int j1, Matrix X) {

        try {
            for (int i = 0; i < r.length; i++) {
                for (int j = j0; j <= j1; j++) {
                    A[r[i]][j] = X.get(i, j - j0);
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
    }

    /**
     * Set a submatrix.
     * 
     * @param r
     *            Array of row indices.
     * @param c
     *            Array of column indices.
     * @param X
     *            A(r(:),c(:))
     * @exception ArrayIndexOutOfBoundsException
     *                Submatrix indices
     */

    public void setMatrix(int[] r, int[] c, Matrix X) {

        try {
            for (int i = 0; i < r.length; i++) {
                for (int j = 0; j < c.length; j++) {
                    A[r[i]][c[j]] = X.get(i, j);
                }
            }
        } catch (ArrayIndexOutOfBoundsException e) {
            throw new ArrayIndexOutOfBoundsException("Submatrix indices");
        }
    }

    /**
     * Solve A*X = B
     * 
     * @param B
     *            right hand side
     * @return solution if A is square, least squares solution otherwise
     */

    public Matrix solve(Matrix B) {

        return (m == n ? (new LUDecomposition(this)).solve(B)
                : (new QRDecomposition(this)).solve(B));
    }

    /**
     * Solve X*A = B, which is also A'*X' = B'
     * 
     * @param B
     *            right hand side
     * @return solution if A is square, least squares solution otherwise.
     */

    public Matrix solveTranspose(Matrix B) {

        return transpose().solve(B.transpose());
    }

    /**
     * Singular Value Decomposition
     * 
     * @return SingularValueDecomposition
     * @see SingularValueDecomposition
     */

    public SingularValueDecomposition svd() {

        return new SingularValueDecomposition(this);
    }

    /**
     * Multiply a matrix by a scalar, C = s*A
     * 
     * @param s
     *            scalar
     * @return s*A
     */

    public Matrix times(double s) {

        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = s * A[i][j];
            }
        }
        return X;
    }

    /**
     * Linear algebraic matrix multiplication, A * B
     * 
     * @param B
     *            another matrix
     * @return Matrix product, A * B
     * @exception IllegalArgumentException
     *                Matrix inner dimensions must agree.
     */

    public Matrix times(Matrix B) {

        if (B.m != n) {
            throw new IllegalArgumentException(
                    "Matrix inner dimensions must agree.");
        }
        Matrix X = new Matrix(m, B.n);
        double[][] C = X.getArray();
        double[] Bcolj = new double[n];
        for (int j = 0; j < B.n; j++) {
            for (int k = 0; k < n; k++) {
                Bcolj[k] = B.A[k][j];
            }
            for (int i = 0; i < m; i++) {
                double[] Arowi = A[i];
                double s = 0;
                for (int k = 0; k < n; k++) {
                    s += Arowi[k] * Bcolj[k];
                }
                C[i][j] = s;
            }
        }
        return X;
    }

    /**
     * Multiply a matrix by a scalar in place, A = s*A
     * 
     * @param s
     *            scalar
     * @return replace A by s*A
     */

    public Matrix timesEquals(double s) {

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                A[i][j] = s * A[i][j];
            }
        }
        return this;
    }

    // DecimalFormat is a little disappointing coming from Fortran or C's
    // printf.
    // Since it doesn't pad on the left, the elements will come out different
    // widths. Consequently, we'll pass the desired column width in as an
    // argument and do the extra padding ourselves.

    /**
     * Matrix trace.
     * 
     * @return sum of the diagonal elements.
     */

    public double trace() {

        double t = 0;
        for (int i = 0; i < Math.min(m, n); i++) {
            t += A[i][i];
        }
        return t;
    }

    /**
     * Matrix transpose.
     * 
     * @return A'
     */

    public Matrix transpose() {

        Matrix X = new Matrix(n, m);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[j][i] = A[i][j];
            }
        }
        return X;
    }

    /*
     * ------------------------ Private Methods ------------------------
     */

    /**
     * Unary minus
     * 
     * @return -A
     */

    public Matrix uminus() {

        Matrix X = new Matrix(m, n);
        double[][] C = X.getArray();
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                C[i][j] = -A[i][j];
            }
        }
        return X;
    }

}
